import math
import numpy as np

class Robot:
    def __init__(self, pos, target_pos, radius, max_speed, max_angular_speed):
        self.pos = pos
        self.target_pos = target_pos
        self.radius = radius
        self.max_speed = max_speed
        self.max_angular_speed = max_angular_speed

    def distance(self, other_robot):
        return np.linalg.norm(self.pos - other_robot.pos)

def virtual_force(robot, other_robots):
    virtual_force = np.zeros(2)
    for other_robot in other_robots:
        if robot != other_robot:
            distance = robot.distance(other_robot)
            if distance <= robot.radius + other_robot.radius:
                # robots are too close, repel
                repulsion = 1 / distance ** 2
                virtual_force += repulsion * (robot.pos - other_robot.pos)
    return virtual_force

def goal_force(robot):
    return robot.target_pos - robot.pos

def calculate_velocity(robot, other_robots):
    virtual_force_vec = virtual_force(robot, other_robots)
    goal_force_vec = goal_force(robot)
    total_force = virtual_force_vec + goal_force_vec
    angle = math.atan2(total_force[1], total_force[0])
    speed = min(np.linalg.norm(total_force), robot.max_speed)
    angular_speed = min(abs(angle), robot.max_angular_speed)
    return speed, angular_speed

def update_robot_position(robot, speed, angular_speed, time_step):
    x = robot.pos[0] + speed * math.cos(robot.direction) * time_step
    y = robot.pos[1] + speed * math.sin(robot.direction) * time_step
    direction = robot.direction + angular_speed * time_step
    robot.pos = np.array([x, y])
    robot.direction = direction

# example usage
robot1 = Robot(np.array([0, 0]), np.array([10, 10]), 0.5, 6, 1)
robot2 = Robot(np.array([1, 1]), np.array([10, 5]), 0.5, 6, 1)
robot3 = Robot(np.array([2, 2]), np.array([5, 5]), 0.5, 6, 1)
robot4 = Robot(np.array([3, 3]), np.array([5, 10]), 0.5, 6, 1)

robots = [robot1, robot2, robot3, robot4]

time_step = 0.02  # 20ms

while True:
    for i, robot in enumerate(robots):
        other_robots = robots[:i] + robots[i+1:]
        speed, angular_speed = calculate_velocity(robot, other_robots)
        update_robot_position(robot, speed, angular_speed, time_step)

    # check for collision
    collision = False
    for i, robot in enumerate(robots):
        for other_robot in robots[i+1:]:
            if robot.distance(other_robot) < robot.radius + other_robot.radius:
                collision = True

